Which stages of the compilation process of an input language solve the problem for priorities in arithmetic expressions (i.e. () -> *,/ -> +,-)? I know that code generators usually exploit Polish notation to produce code for a stack machine. But is it necessary to regard the priorities of operations into the grammar of the language syntax?
I am not a authority in this area, but from my undergrad understanding, I would understand that it is necessary to incorporate priorities in language. Priority of operations are semantic attribute and translation (read compilation) require to translate such information into machine code.
Let we consider the following sample.
2+2*2
Let it be
2+(2*2)=6
Braces shows that multiplication has higher priority.
In case of
(2+2)*2
the answer is 8.
Thus, is it necessary to regard the priorities of operations?
If you meant "should I regard it in my grammar or in my code"... Well, it actually doesn'y matter.
Colleageus, thanks all of you! Special thanks to Mr. Breuer for the detailed answers! I have explained myself, that priorities of operations are considered in the code generation stage. Expressing priorities in the grammar is description for the language users.
The final computation must reflect the relative priorities (or precedence) of the arithmetic operators, as Klishinsky points out. That is a requirement for correctness.
Typically, in an LL, LR, or recursive descent parser, that notion of precedence is implicit in the grammar for the language. In an operator precedence parser, that precedence is encoded explicitly in one or more tables that the parser uses to determine its next action. In any of these situations, the parser generates an abstract representation that encodes that precedence -- usually in an explicit way, such as the structure of an expression tree or the specific sequence of operations in some linear representation.
After that, precedence is rarely an issue, because it is encoded directly into the representation on which the compiler operates. Precedence can again become an issue if the compiler tries to refactor the computations. (The compiler might refactor a computation to enhance opportunities for parallelism, at one of several levels ranging from instruction level parallelism to SIMD parallelism to multi-threaded computation. Refactoring can also be used to enhance the value of other optimizations, in which case it is typically referred to as "reassociation" -- the application of commutativity, associaitivity, and/or distributivity to rearrange an expression.)
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